The invention concerns a method for magnetic resonance (MR) imaging for imaging an imaging area of an object, wherein a spatial MR signal distribution with a background phase distribution is generated, MR signals are acquired, the spatial MR signal distribution is reconstructed, and an MR image is stored and/or displayed, wherein the reconstruction quality depends on the spatial distribution of the background phase, and wherein the background phase distribution to be generated is determined by means of an optimization algorithm with the reconstruction quality as optimization criterion.
A method of this type is disclosed e.g. by reference [1].
Magnetic resonance imaging (MRI), which is also called magnetic resonance tomography (MRT), is a widely used technology for non-invasive acquisition of images of the inside of an object under investigation and is based on spatially resolved measurement of magnetic resonance signals from the object under investigation. By subjecting the object under investigation to a substantially static and homogeneous magnetic basic field (also called the main magnetic field) within the measuring volume of a magnetic resonance measuring apparatus, the nuclear spins contained in the object under investigation are oriented with respect to the direction of the basic field, generally selected as the z direction of a magnet-bound coordinate system. The associated orientation of the magnetic dipole moments of the atomic nuclei results in magnetization within the object in the direction of the main magnetic field, which is called longitudinal magnetization. In the MR investigation (MR: magnetic resonance), this magnetization within the object under investigation is excited into a precession movement, the frequency of which is proportional to the local magnetic field strength, through irradiation of electromagnetic RF pulses (RF: radio frequency) using one or more RF transmitting elements of a transmitting antenna device. The vector of magnetization is thereby deflected from the equilibrium position (z direction) through an angle, which is referred to below as the deflection angle.
In the MRI methods used nowadays, a spatial encoding is impressed on the precession movements of the nuclear spins for all three spatial directions through time-variant superimposition of additional spatially dependent magnetic fields, which are referred to below as additional magnetic fields. These additional magnetic fields usually comprise substantially constant gradients of the z component in the spatial directions x, y, and z within the object under investigation, and are generated by a coil configuration, which is referred to as a gradient system, the coils being controlled by one so-called gradient channel for each spatial direction. However, for some years there have been different imaging technologies which also use non-linear additional magnetic fields with spatially varying gradients. In the following, linear and non-linear magnetic fields always refer to the spatial dependence of the z component of the fields unless otherwise specified. Spatial encoding is usually described by a scheme in a space conjugated from the position space via Fourier transformation, the so-called k space. Switching of additional magnetic field pulses can be described as passage of a trajectory in k space, the so-called k space trajectory in this k space formalism. This can only be applied when magnetic fields are used having a spatially constant gradient, wherein data is acquired as described below at certain points in k space determined by the spatial encoding scheme. The density of these data points and the extension of the amount of data points in k space determine the so-called “field of view” or spatial resolution with which the object under investigation or parts thereof are imaged.
The transverse component of the precessing magnetization associated with the nuclear spins (also called transverse magnetization below) induces electric voltage signals (which are also called magnetic resonance signals (MR signals)) in one or more RF receiving antennas which surround the object under investigation. Time-variant magnetic resonance signals are generated by means of pulse sequences, which contain specially selected sequences of RF pulses and additional magnetic field pulses (temporary application of time-constant or time-variant additional magnetic fields) in such a fashion that they can be converted into corresponding spatial images. According to one of a plurality of well-known reconstruction technologies, this is realized after acquisition, amplification and digitization of the MR signals using an electronic receiver system, processing thereof by means of an electronic computer system, and storage thereof in one-dimensional or multidimensional data sets. The pulse sequence used typically contains a sequence of measuring processes called spatial encoding steps in which the gradient pulses are varied in accordance with the selected spatial encoding method. The number of spatial encoding steps and the duration thereof, except for averagings and repetitions, substantially determine the duration of an MR imaging experiment.
Parallel Imaging (PI) in MRT was first presented in 1997 (reference [2]) and is based on the use of RF receiving antenna arrays which consist of several antenna elements for simultaneous data acquisition, the spatial variation of the receiving sensitivity (sensitivity) of which is used for additional spatial encoding of the MR signal. Parallel imaging enables reduction of the number of acquired data points in k space and associated reduction of the number of acquired data points in k space and therefore reduction of the acquisition time, while maintaining the resolution with respect to space and time or increasing the resolution with respect to space and time for identical acquisition time. The reduction of the acquired data points by a reduction factor R is associated with subsampling of k space, i.e. in parallel imaging not all data points are measured which would be required for complete sampling of k space according to Nyquist. This results in spatial convolution of the images in standard Fourier reconstruction. Parallel imaging algorithms, however, utilize the spatial information contained in the sensitivities in order to either supplement the missing data in k space (e.g. GRAPPA, reference [3]) or eliminate the convolution artefacts in the image space (e.g. SENSE, reference [4]).
One problem with the implementation of such PI technologies is the fact that use of parallel imaging with increasing reduction factors results in a considerable increase in reconstruction artefacts in the images and also in a dramatic drop in signal-to-noise ratio (SNR) in the reconstructed images. This SNR drop substantially has two reasons. On the one hand, in MRT the SNR is generally proportional to the square root of the number of acquired data points. On the other hand, in parallel imaging additional noise increase often occurs as a result of the frequently poor numerical conditions of the parallel re-construction problem. In a SENSE reconstruction, this noise increase can be quantitatively described for each point in the image in a simple fashion via the so-called local geometry factor (g factor) (see also reference [4]). This simple analytic description of the noise gain is not possible with GRAPPA, however, there are also methods for quantifying the noise increase for this case (reference [12]).
In order to be able to further increase the reduction rates or reduce the noise increase, a number of improved parallel imaging methods have been developed in recent years, which e.g. combine PI with partial Fourier imaging (e.g. reference [5]) or utilize complexly conjugated symmetry relations in k space by using a priori knowledge about the image phase in the PI reconstruction process (e.g. reference [6]). A further method which is based on such complexly conjugated symmetry relations is the so-called Virtual Coil Concept (reference [1]). This method calculates “virtual MR signals” from “virtual receiving antennas”. These signals then consist of complexly conjugated symmetrical signals of the real receiving antennas and contain additional phase information. The integration of this additional virtual data in the PI reconstruction process contributes to an improvement in the numerical conditions of reconstruction.
One common property of all above-explained methods is that the spatial dependence of the so-called background phase of the MR signal distribution has a significant influence on the degree of improvement of the reconstruction quality that can be achieved, thereby e.g. reducing the noise increase. MR signal distribution in this context means the transverse magnetization that is present in the object under investigation at the time of data acquisition. The background phase thereby defines that phase which would contain the MR signal distribution without taking into consideration the phase portion which is generated through spatial encoding using additional magnetic fields and which is again eliminated through decoding within the scope of conventional reconstruction methods.
The influence of the background phase on the reconstruction quality will be exemplarily explained below on the basis of the “Virtual Coil Concept”.
In an MR imaging experiment with several receiving antennas, the k space signal S3(k) received by antenna j (j=1 . . . m) is represented below:Sj(k)=∫d×ρ(x)eiφ(x)Cj(x)e−ikx   (1)wherein ρ(x) and φ(x) designate the real amplitude and the back-ground phase of the spatial MR signal distribution and Cj(x) designates the complex spatial receiving sensitivity (sensitivity) of the receiving antenna. One can now introduce a so-called effective sensitivity Dj(x)=eiφ(x)Cj(x) for each antenna by combining the background phase with the sensitivity. In this fashion Sj(k) can be written as Fourier transform of the spatial signal distribution multiplied by the effective sensitivitySj(k)=FT└ρ(x)Dj(x)┘  (2)
Considering now the symmetrical complexly conjugated k space signal, one obtains the following, since ρ(x) is a purely real quantity:Sj*(−k)=∫d×ρ(x)e−iφ(x)Cj*(x)ei(−k)x   (3)wherein “*” designates the operation of complex conjugation.
By now introducing a second set of m so-called “virtual coils”, the effective sensitivities of which are defined by Dv(x)=Dj*(x)=e−iφ(x) Ci*(x), with v=j+m, a second set of k space data can be introduced, which corresponds to the symmetrical complexly conjugated k space data of the real coils and which can now be represented as Fourier transforms of the spatial signal distribution multiplied by the effective sensitivities of the virtual coils:Sv(k)=Sj*(−k)=FT[ρ(x)Dj*(x)]FT[ρ(x)Dv(x)]  (4)
These relationships clearly show that when k space data of these virtual coils is used in the PI reconstruction process, additional information is introduced into this process, thereby contributing to an improvement of the condition which is generally given with Dj(x)≠Dj*(x) and which means that the effective sensitivity of the real coils must not be purely real. The degree of improvement of the condition by this means depends on the detailed spatial dependence of the phase of the effective sensitivities. Since the background phase of the MR signal distribution is an essential component of the phase of the effective sensitivities, specific manipulation of this background phase can optimize the condition of the reconstruction problem. This applies, except for the “Virtual Coil Concept”, in a similar fashion also for the other above-mentioned improved PI methods. At this point, it has to be mentioned that manipulation of the background phase improves the reconstruction quality not only for parallel imaging. There are special cases, in which such an optimized background phase also improves the reconstruction when only one receiving antenna is used. For example, when only one individual antenna is used for reception, the use of the “Virtual Coil Concept” is analogous to the application of a “Half-Fourier” reconstruction. Numerous experimental parameters are included in the background phase, such as the properties of the imaging sequence used (e.g. number, flip angle and phase of the RF pulses used, echo times, applied additional magnetic fields), physical parameters in the object under investigation (e.g. off resonances due to field inhomogeneities or chemical shift) and last but not least properties of the emitting antennas (e.g. spatial phase distribution of the magnetic transmitting field). This versatile dependence of the background phase therefore also provides the possibility of influencing the spatial distribution thereof during an imaging experiment, thereby improving the reconstruction quality.
In practice, a dependence of the background phase must be initially determined for this purpose, thereby utilizing the dependence between reconstruction quality and background phase distribution by means of an optimization algorithm, which optimizes the reconstruction quality. In a further step, this background phase dependence would then have to be impressed on the spatial MR signal distribution in an experiment.
Despite the above-described versatile dependencies of the background phase, there is currently no prior art method for experimentally realizing complexly formed background phase distributions which would often be necessary for an optimum reconstruction quality.
This is, in particular, due to the fact that the phase dependencies resulting from optimization methods according to prior art (e.g. reference [1]) often have very small-scale phase variations, numerous phase jumps and, in the extreme case, noise-like patterns which cannot be experimentally utilized in this form. As a result thereof, reference [1] states that the optimum phase distributions could not be generated and applied in actual experiments so far.
It is therefore the underlying purpose of the present invention to present a method which provides an improved reconstruction quality in comparison with conventional imaging methods with standard reconstruction, and at the same time can be realized with means that are available.